# Error Control and Loss Functions for the Deep Learning Inversion of Borehole Resistivity Measurements

arXiv: https://arxiv.org/abs/2005.08868 · HTML: https://mlsanity.com/paper/2005.08868/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 May 2020.

## Built on by (most cited first, 8 of 8)

- [Physics Embedded Machine Learning for Electromagnetic Data Imaging](https://mlsanity.com/paper/2207.12607/) (2022)
- [Probabilistic model-error assessment of deep learning proxies: an application to real-time inversion of borehole electromagnetic measurements](https://mlsanity.com/paper/2205.12684/) (2022)
- [Direct multi-modal inversion of geophysical logs using deep learning](https://mlsanity.com/paper/2201.01871/) (2021)
- [Optimal Sequential Decision-Making in Geosteering: A Reinforcement Learning Approach](https://mlsanity.com/paper/2310.04772/) (2023)
- [High-Precision Geosteering via Reinforcement Learning and Particle Filters](https://mlsanity.com/paper/2402.06377/) (2024)
- [LLM-Based Test Oracles: Source-of-Authority Taxonomy -- A Systematic Literature Review](https://mlsanity.com/paper/2607.05031/) (2026)
- [Design of borehole resistivity measurement acquisition systems using deep learning](https://mlsanity.com/paper/2101.05623/) (2021)
- [Automated machine learning for borehole resistivity measurements](https://mlsanity.com/paper/2207.09849/) (2022)

## Abstract (arXiv)

Deep learning (DL) is a numerical method that approximates functions. Recently, its use has become attractive for the simulation and inversion of multiple problems in computational mechanics, including the inversion of borehole logging measurements for oil and gas applications. In this context, DL methods exhibit two key attractive features: a) once trained, they enable to solve an inverse problem in a fraction of a second, which is convenient for borehole geosteering operations as well as in other real-time inversion applications. b) DL methods exhibit a superior capability for approximating highly-complex functions across different areas of knowledge. Nevertheless, as it occurs with most numerical methods, DL also relies on expert design decisions that are problem specific to achieve reliable and robust results. Herein, we investigate two key aspects of deep neural networks (DNNs) when applied to the inversion of borehole resistivity measurements: error control and adequate selection of the loss function. As we illustrate via theoretical considerations and extensive numerical experiments, these interrelated aspects are critical to recover accurate inversion results.